Energy harvesting in the super-harmonic frequency region of a twin-well oscillator

Nonlinear dynamical systems exhibit super-harmonic resonances that can activate large-amplitude motions at fraction integers of the fundamental frequency of the system. Such resonances offer a unique and untapped opportunity for harnessing vibratory energy from excitation sources with low-frequency components. To that end, this paper exploits the super-harmonic frequency bands of a nonlinear twin-well (bi-stable) oscillator for harvesting energy from low-frequency excitations. Theoretical and experimental studies are performed on an axially loaded clamped-clamped piezoelectric beam harvester with bi-stable potential characteristics. Voltage- and power-frequency bifurcation maps are generated near the super-harmonic resonance of order two. It is shown that, for certain base acceleration levels, the harvester can exhibit responses that are favorable for energy harvesting. These include a unique branch of large-orbit periodic inter-well oscillations, coexisting branches of large-orbit solutions, and a bandwidth of frequencies where a unique chaotic attractor exists. In these frequency regions, the harvester can produce power levels at half its fundamental frequency that are comparable to those obtained near the fundamental frequency.